Interest Rate as the Sum of Real Risk-free Rate and Risk Premiums

Interest is a reward a borrower pays for using an asset, usually capital, belonging to a lender. It is compensation for the loss or value depreciation occasioned by the use of the asset. We could also describe it as the opportunity cost of alternative investments.

At the time of lending, the lender most likely has a portfolio of investment vehicles to choose from. As such, they must charge a premium for the ‘loss’ of the alternative investment opportunities. We express interest as an annual percentage, from which we can calculate monthly, quarterly, or semi-annual equivalents. The level of interest rate is a function of several risks.

Therefore, an interest rate is composed of a real risk-free interest rate plus a set of four premiums that represent compensation for bearing distinct types of risk:

$$ \begin {align*}
r & = \text {Risk free rate} + \text {Inflation premium} \\
& +\text {Liquidity premium} + \text {Maturity premium} \\
& + \text {Default premium}
\end {align*} $$

Where \(r\) is the interest rate.

The Risk-free Rate

The risk-free rate is the rate of return that assets largely considered risk-free offer. Such assets usually include government securities or local authority bonds. The real risk-free interest rate is the single-period return on a risk-free security assuming zero inflation.

Types of Risk Premiums

Inflation Risk Premium

Inflation risk is the loss of purchasing power of money as a result of the increase in prices of consumer goods. The inflation risk premium is the additional return that investors demand aside from the real risk-free rate. The risk of a decrease in purchasing power validates the inflation risk premium.

Liquidity Risk Premium

Liquidity refers to the ease with which an investment can be converted into cash without significantly sacrificing market value. Liquidity risk premium refers to the additional return that an investor demands from any investment that cannot liquidate instantly for cash in the market.

Default Risk Premium

Default risk describes a situation where a borrower may fail to repay borrowed funds as a result of bankruptcy. This might result in significant losses on the side of the lender. A default premium is an additional return required by the lender or investor from a borrower for their (lender’s) assumption of default risk.

Maturity Risk Premium

Maturity risk premium is the additional return an investor requires for assuming interest rate and reinvestment risk resulting from a longer investment maturity timeline. Maturity risk premium increases with an increase in the maturity timeline. In other words, the longer the maturity timeline of an investment, the higher the maturity risk premium.

Question

Which of the following statements is the most accurate about interest rates?

A. The risk-free rate is the rate of return that assets such as corporate bonds largely considered risk-free offer.

B. Inflation risk describes a situation where a borrower may cease to repay borrowed funds as a result of bankruptcy.

C. The interest rate formula includes the risk-free rate, default premium, liquidity premium, inflation premium, and maturity premium.

Solution

The correct answer is C.

You must add the four types of risks to the risk-free rate to come up with the overall rate of interest, r.

A is incorrect. The risk-free rate is the rate of return that assets largely considered risk-free, such as government securities, offer.

B is incorrect. Inflation risk is the loss of purchasing power of money as a result of the increase in prices of consumer goods.